1. 1 Future of Abstraction Alexander Stepanov

2. 2 Outline of the Talk Outline of the Talk  What is abstraction?  Abstraction in programming  OO vs. Templates  Concepts  A new programming language?

3. 3 AbstractionAbstraction  The fundamental way of organizing knowledge  Grouping of similar facts together  Specific to a scientific discipline

4. 4 Abstraction in Mathematics Abstraction in Mathematics Vector space {V: Group; F: Field; ×: F, V → V; distributivity; distributivity of scalars; associativity; identity} Algebraic structures (Bourbaki)

5. 5 Abstraction in Programming Abstraction in Programming for (i = 0; i < n; i++) sum += A[i];  Abstracting +  associativity; commutativity; identity  parallelizability ; permutability; initial value  Abstracting i  constant time access; value extraction

6. 6 1.Take a piece of code 2.Write specifications 3.Replace actual types with formal types 4.Derive requirements for the formal types that imply these specifications Abstraction in Programming

7. 7 Abstraction Mechanisms in C++  Object Oriented Programming  Inheritance  Virtual functions  Generic Programming  Overloading  Templates Both use classes, but in a rather different way

8. 8 Object Oriented Programming  Separation of interface and implementation  Late or early binding  Slow  Limited expressability  Single variable type  Variance only in the first position

9. 9 Class reducer Class reducer class reducer { public: virtual void initialize(int value) = 0; virtual void add_values(int* first, int* last) = 0; virtual int get_value() = 0; }; class sequential_reducer : public reducer { … }; class parallel_reducer : public reducer { … };

10. 10 Generic Programming Generic Programming  Implementation is the interface  Terrible error messages  Syntax errors could survive for years  Early binding only  Could be very fast  But potential abstraction penalty  Unlimited expressability

11. 11 Reduction operator Reduction operator template typename iterator_traits ::value_type reduce(InputIterator first, InputIterator last, BinaryOperation op) { if (first == last) return identity_element(op); typename iterator_traits ::value_type result = * first; while ( ++ first != last) result = op(result, * first); return result; }

12. 12 Reduction operator with a bug template typename iterator_traits ::value_type reduce(InputIterator first, InputIterator last, BinaryOperation op) { if (first == last) return identity_element(op); typename iterator_traits ::value_type result = * first; while ( ++ first < last) result = op(result, * first); return result; }

13. 13 We need to be able to define what InputIterator is in the language in which we program, not in English

14. 14 Concepts Concepts concept SemiRegular : Assignable, DefaultConstructible{}; concept Regular : SemiRegular, EqualityComparable {}; concept InputIterator : Regular, Incrementable { SemiRegular value_type; Integral distance_type; const value_type& operator*(); };

15. 15 Reduction done with Concepts Reduction done with Concepts value_type(InputIterator) reduce(InputIterator first, InputIterator last, BinaryOperation op ) (value_type(InputIterator) == argument_type(BinaryOperation)) { if (first == last) return identity_element(op); value_type(InputIterator) result = * first; while ( ++ first != last) result = op(result, * first); return result; }

16. 16 Signature of merge Signature of merge OutputIterator merge(InputIterator[1] first1, InputIterator[1] last1, InputIterator[2] first2, InputIterator[2] last2, OutputIterator result) (bool operator<(value_type(InputIterator[1]), value_type(InputIterator[2])), output_type(OutputIterator) == value_type(InputIterator[1]), output_type(OutputIterator) == value_type(InputIterator[2]));

17. 17 Virtual Table for InputIterator Virtual Table for InputIterator  type of the iterator  copy constructor  default constructor  destructor  operator=  operator==  operator++  value type  distance type  operator*

18. 18 Unifying OOP and GP Unifying OOP and GP  Pointers to concepts  Late or early binding  Well defined interfaces  Simple core language

19. 19 Other Language Problems  Semantic information:  assertions, complexity  Multiple memory types:  pointers, references, parameter passing  Compilation model:  cpp, includes, header files  Design approach:  evolution vs. revolution

20. 20 ConclusionConclusion We have to create a language that expresses everything we want to say about computations: If it is worth saying, it is worth saying formally.